Bow every time. My cousin recently made from from yew with a set of six arrows. The arrowheads were made from stainless teaspoons.
We don't yet know the power of the bow in official terms, but it is far far more penetrative and harmful than either my .17HMR or my .22 rimmy over comparable ranges, whilst also being silent and sustainably renewable.

200 or so metres is a fair distance to make em cautious at ,especially if you are going to have to fetch em back for dinner(ps close and a precise kill is good for bow hunting)

carrying irreplaceable high tech stuff that fails as soon as how much can you carry runs out or it goes rusty or requires a good chemist and another 50kg of reload kit to make it work again once the expendables are expended

i could make a case for a brown bess (if you are a good chemist and fair smith )or a sort of good case for an ak(if you can "forage consumables" and do a bit of smithing ) but long term without an "industrial" support and supply structure bow is queen.

high tech stuff is very good at what it does when constantly supported by high tech infrastructure ,spot the weakness

bow is easier to learn than precision engineering and good chemistry as well

Bow every time. My cousin recently made from from yew with a set of six arrows. The arrowheads were made from stainless teaspoons.
We don't yet know the power of the bow in official terms, but it is far far more penetrative and harmful than either my .17HMR or my .22 rimmy over comparable ranges, whilst also being silent and sustainably renewable.

as well as the delivered energy the messiness of a sharp n jagged broad head adds to the wound track and can be relevant
the terminal ballistics of even a light (25lb pull) bow which a kid can use can do far more to give a lethal effects on game or zombies than most hard rounds (even hv ones) with the right head

re delivered energy in imperial a rough estimate is 2/3 draw weight x draw length for "muzzle energy"
the travelling and terminal ballistics are complicated as the "round" is massive and wobbly as well as either pointy or bladey or both .

the springyness/speed of the bow and stiffness of the arrow do matter ie for a given pull the faster the bow goes strait and the less bent the arrow gets at launch the more energy sets off .
it is more complex than it might seem.

the best way to assess performance is by the wound track in a variety of targets with a variety of arrows

a neat hole wont drop a bear although it might have a problem putting its pajamas on

If you're talking about zombies then I'll just have a laser gun with limitless charge as we're living in a fantasy world.

If you're talking about bow hunting, in places where it's legal, then for example it seems most US bow hunters will only hunt out to 35 yards (often 20 yards is typical) and that's with very powerful modern compound bows.